6. See the market behave like a sand dune in wind

Sand Storm! 2010: Act I, Scene 6; A Market Behaves Like a Sand Dune in Wind.

This simile draws an analogy, rather than claiming to be an integral feature of the DiligentInvestor econometric model. The analogy has rather more physical force than the swarm or flock behavior suggested earlier, as the physics of blown sand and desert dunes is being worked out in both theory and experiment, while we have yet to measure the intentions of bees or sheep. There is indeed a central force law expressed about a sand dune, in that the dune lofts the wind over itself, perturbing the flow in plan view so that more sand is brought toward the dune. Individual grains settle in such a way as to keep the surface smooth except for regular ripples, so that the grains of a given size fraction become uniformly spaced. The dune removes sand from its neighborhood as well, so all three laws of the flock are present. And dunes are sufficiently universal that they have been seen on Mars.

In the economic environment, Hoteling's law states that the best place to put a gas station is right across the intersection from an existing gas station. Generalized a little bit, this suggests the flocking law of uniform distance among nearest neighbors. In another interpretation, two stocks with identical risk and return are competitors, except for correlations with other stocks, so they tend to move away from one another enough to be distinguished by the investor. The observed consistent velocities of stocks in normal space also makes sense for this analogy in that sand grains have a very definite saltation velocity distribution that depends upon the wind speed. Perhaps most convincing is the observation that the type of sand dune called barchan illustrates the same crescent shape as shown by the purple curve marking the highest density. Therefore, we take the surface shown by the contour map described on the prior page, turn it to get an oblique perspective view, and illustrate its changes as in the Dune Snapshot taken from the animation. Note that the global velocity arrow and clock appear in oblique perspective as well, so the 1 January tic-mark is above and to the right of the year hand. The heavy contour line in the previous part of the animation is the same as the "waterline" around the dune. Most of the illumination comes from low on the right. Wherever the dune surface is decreasing in height and eroding, the color gradually gets darker, until the surface next increases in height as if covered with a freshly deposited layer of sand. As a guide to the eye, perpendicular silhouettes of the dune appear on the walls in back and to the left, with the instantaneous peak marked. The same mean and standard deviation lines are drawn on the floor, and a vertical line is drawn upward from the origin.

What does this analogy mean for the investor? The physical laws and numerical values of operational parameters describing sand dune evolution are only recently becoming clear. Among these physical models, there are strong hints of structure that apply to the market as well. Therefore, the analogy offers some hope that these physical models may be useful in describing the market, as has been the case for the diffusion theory that underlies option pricing, or the statistical mechanics behind successful day trading. Another degree of hope is offered by the observation that not all stocks move in the direction of the average, just as some sand grains are splashed upwind in a sand storm. More immediately, it suggests that there may be good reasons for the measurable behavior illustrated in the Blu-ray and in the DiligentInvestor Screener, and consequently an investing opportunity.

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